Observation of Reentrant Correlated Insulators and Interaction-Driven Fermi-Surface Reconstructions at One Magnetic Flux Quantum per Moiré Unit Cell in Magic-Angle Twisted Bilayer Graphene

The discovery of flat bands with nontrivial band topology in magic-angle twisted bilayer graphene (MATBG) has provided a unique platform to study strongly correlated phenomena including superconductivity, correlated insulators, Chern insulators, and magnetism. A fundamental feature of the MATBG, so far unexplored, is its high magnetic field Hofstadter spectrum. Here, we report on a detailed magnetotransport study of a MATBG device in external magnetic fields of up to $B=31\mathrm{T}$, corresponding to one magnetic flux quantum per moiré unit cell ${\mathrm{\Phi }}_0$. At ${\mathrm{\Phi }}_0$, we observe reentrant correlated insulators at a flat band filling factors of $\nu =+2$ and of $\nu =+3$, and interaction-driven Fermi-surface reconstructions at other fillings, which are identified by new sets of Landau levels originating from these. These experimental observations are supplemented by theoretical work that predicts a new set of eight well-isolated flat bands at ${\mathrm{\Phi }}_0$, of comparable band width, but with different topology than in zero field. Overall, our magnetotransport data reveal a qualitatively new Hofstadter spectrum in MATBG, which arises due to the strong electronic correlations in the reentrant flat bands.

Figure 1

(a) Schematic of the MATBG device with the performed measurement scheme of the back-gated four-terminal $R_{xx}$ and $R_{xy}$ measurements. The twist angle of the device is $\theta =1.12°\pm 0.02°$, which results in $B_0=30.5\mathrm{T}$. (b) Band structure at zero and ${\mathrm{\Phi }}_0$ magnetic flux. (c) Color plot of $R_{xx}$ as a function of $\nu$ and $B$ measured at $T=40\mathrm{mK}$ around $\nu =2$, showing the reentrant CI and emergence of LLs. (d) $R_{xx}$ vs $\nu$ over the entire range of the flat band at $B=0\mathrm{T}$ and $B=30\mathrm{T}$, clearly showing the reentrant CI at $\nu =+2$ close to ${\mathrm{\Phi }}_0$. (e) and (f) $R_{xx}$ and $R_{xy}$ as a function of $\nu$ at $B=22\mathrm{T}$ and $B=5\mathrm{T}$, respectively, showing full quantization of the ${\nu }_L=+2$ LL gap.

Figure 2

(a) and (b) show, respectively, the color plots of $R_{xx}$ and $R_{xy}$ as a function of $B$ and $v$, for the full magnetic phase space from $B=0\mathrm{T}$ to $B=31\mathrm{T}$ and $v$ from $-4$ to 4. (c) Schematics of all the LLs emerging from different fillings of the band from both zero flux and ${\mathrm{\Phi }}_0$. Light blue lines from the CNP indicate the LLs with ${\nu }_L=\pm 1$, $\pm 2$, $\pm 3$, $\pm 4$, and $\pm 5$. Dark blue lines indicate the LLs from $\nu =\pm 1$ at both zero flux and ${\mathrm{\Phi }}_0$. Dark red lines correspond to LLs from $v=\pm 2$ at both zero flux and ${\mathrm{\Phi }}_0$. Orange lines indicate the LLs that emerge from $\nu =\pm 3$ and purple lines correspond to LLs from $\nu =-4$. Solid lines mark well-pronounced, quantized LLs, while dashed lines mark much weaker, nonquantized levels.

Figure 3

(a) Calculated Hofstadter spectrum of the BM model for positive energy as a function of the magnetic flux $\mathrm{\Phi }$ through the moiré unit cell. Different solid gray (4, 0), blue (4, 4), red (4, 12), yellow (8, 4), green (8, 8), cyan (8, 12), magenta (8, 16) and purple (4, 20) regions correspond to the evolution of dominant LL gaps. They are marked with the band filling and filling factor of the LLs $(\nu ,{\nu }_L)$. (b) Color plot of $\log (R_{xx})$ as a function of $B$ and $v$ for high range of carrier density up to $\nu =16$. (c) Schematics of (b) and the comparison with (a), where gray circles mark the theoretically predicted gaps from (a) and colored lines mark the strongest LLs in (b). The observed LLs from (b) are plotted with the same color code as the corresponding LLs in (a). Dark gray lines correspond to LLs, which are not predicted from the Hofstadter calculations. These levels are the result of strong interactions in the system (${\nu }_{\text{Lint}}$). The horizontal blue bars denote metallic regions in (a) matching the high conductance regions (dark blue regions) observed in (b).